The Summon negation window is an unofficial term for the activation timing of cards that negate the Summon of a monster, such as "Solemn Warning", "Solemn Judgment", "Black Horn of Heaven", "Evolzar Laggia", "Thunder King Rai-Oh", "Royal Oppression", etc.
This timing is before the Summon response window. If the monster's Summon was negated in the Summon negation window, there will not be any Summon response window afterwards.
Only cards that negate Summons can start the Chain during this window, so "Mystical Space Typhoon" cannot be activated as Chain Link 1 of the Summon negation window, but it can be activated as Chain Link 2 if a card like "Royal Oppression" was activated first. Cards like "Bottomless Trap Hole", "Trap Hole", etc. that respond to the Summon of a monster cannot be activated during this window; they can only be activated in the Summon response window.
The Summon negation window will only open if a monster would be Normal Summoned, Flip Summoned, Synchro Summoned, Xyz Summoned, Pendulum Summoned, or Special Summoned with a Special Summoning condition, and only when they occur outside of a Chain. For example, the Normal Summon of a monster with "Ultimate Offering" cannot be negated if it was Chained to "Pot of Greed" (as the monster is Summoned in the middle of a Chain), but it can be negated if "Ultimate Offering" is activated as Chain Link 1 (as the monster is Summoned immediately after the effect of "Ultimate Offering" resolves).
If a monster is Special Summoned with a card effect, the monster is Summoned during the resolution of the effect, not an as action outside of a Chain, so this window never opens.
During the Summon negation window, a monster is not considered to be on the field as it has not yet been Summoned (even if it is being Flip Summoned or is a Gemini monster being Normal Summoned again), so any Continuous Effects it has are not yet active and it is unaffected by any effects that only apply to it while it is on the field (however, any Equip Cards equipped to it are not destroyed unless the Summon is negated). If the monster is moved to a different location during this window, it is not considered to have been moved from the field; for example, if a monster's Summon is negated by "Forced Back" while "Degenerate Circuit" is active, that monster is returned to its owner's hand and not banished, because it was not on the field when it was returned.
If a Summon is negated, the monster was not successfully Summoned, so Special Summon-only monsters cannot be Special Summoned by effects other than their specified method. However, the Summon still counts as the one Normal Summon/Set per turn even if negated.
In the Summon negation window, due to Fast Effect Timing, the turn player can activate cards that negate the Summon of a monster before the opponent can, such as "Solemn Warning", to negate the Summon of his own monster, though this is almost never seen.
The Summon negation window is open now, and player A can activate cards that negate the Summon of a monster, such as "Solemn Warning", "Solemn Judgment", "Black Horn of Heaven", etc. If player A passes doing so, then player B has the opportunity to do the same.
If player B successfully activates one of such cards, the Summon of "Black Luster Soldier - Envoy of the Beginning" will be negated, and it will not be considered to have been Summoned (so it cannot later be Special Summoned by a card like "Monster Reborn"). The monsters banished to Summon "Black Luster Soldier - Envoy of the Beginning" stay banished, even though the Summon was negated.
If player B passes without playing any such cards, "Black Luster Soldier - Envoy of the Beginning" will be successfully Summoned. Now the Summon negation window is closed and the Summon response window is opened.
There is only one Chain in the Summon negation window. After that, no card that negates the Summon of a monster (such as "Solemn Warning") can be activated.